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  4. The value of cos (2 cos -10.8) is

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Q. The value of $ \cos (2{{\cos }^{-1}}0.8) $ is

JamiaJamia 2009

Solution:

Since, $ 2{{\cos }^{-1}}x={{\cos }^{-1}}(2{{x}^{2}}-1) $ Therefore, $ 2{{\cos }^{-1}}0.8={{\cos }^{-1}}(2\times 0.64-1)={{\cos }^{-1}}(0.28) $ $ \Rightarrow $ $ \cos (2{{\cos }^{-1}}0.8)=\cos ({{\cos }^{-1}}0.28)=0.28 $